Wavelength-tunable ultrafast light sources, with tunability far beyond the gain bandwidth of (a limited number of) naturally available laser media, enable a great variety of applications ranging from bio-spectroscopy [1–3] to safety inspection [4]. Presently available solutions, such as optical parametric generation (OPG), can provide laser emission extending from the ultraviolet (UV) to the mid-infrared (MIR) [5,6]. However, the need for (intra-cavity) mechanical readjustment for wavelength tuning results in operational reliability issues, limiting the applications of OPG sources outside dedicated optical laboratories. On the other hand, supercontinuum (SC) fiber lasers usually have simple configuration and are operationally robust [7,8]. However, for many applications, efficient power conversion in SC technology usually conflicts with the strict requirement on low noise [9], affecting negatively the system stability and precluding acceptably fast measurements.

Fiber-optic Cherenkov radiation (FOCR), also known as dispersive wave generation [10] or non-solitonic radiation [11], is a remarkably efficient process, in which one can convert the wavelength of a standard mode-locked pump laser (e.g., Yb-, Er-, or Tm-fiber laser) to almost any target wavelength. Unlike SC generation, the in-fiber Cherenkov process allows for wavelength conversion in a spectrally isolated, resonant fashion, at modest pump pulse energies, and with low noise [12]. In this process, soliton compression of sub-picosecond pump pulses in a fiber with anomalous dispersion at the pump wavelength leads to the emission of a dispersive wave, or FOCR, at a wavelength determined by the phase matching to the soliton wavenumber [13]. As illustrated in Fig. 1(a), by varying the photonic crystal fiber (PCF) dispersion profile, and thus the FOCR phase-matching condition by controlling the lateral dimension of a PCF structure, one can easily tune the resulting FOCR wavelength over a broad spectral range. A number of groups have utilized this flexibility to obtain efficient generation of relatively narrowband, spectrally isolated FOCR pulses in the visible and UV ranges [14–22].

Because of its straightforward implementation and good noise figure, FOCR generation has been successfully used in bio-photonics, including such demanding applications as biomedical imaging [23]. However, the ultimate challenge of achieving continuous ultra-broadband laser tunability still stands: in all systems demonstrated to date, the FOCR wavelength was fixed to within a few tens of nanometers [22] by the specific dispersion of the fiber and the wavelength of the pump laser. However, for many applications, a much wider tunability is desired, e.g., for fluorescence spectroscopy, one might want a single source spanning the entire visible region. Discrete wavelength switching could be achieved by manually changing between the PCFs with different dispersion profiles [15,16,19], or, equivalently, by switching between the pump lasers with different pump wavelengths [18]—a demanding task for a practical implementation of this technique. True arbitrary wavelength generation—spectrally continuous wide-range laser tunability, was still unattainable [14,24].

In this work, we demonstrate a novel widely tunable femtosecond fiber laser based on FOCR in tapered PCFs pumped by a Yb-based femtosecond laser whose power and pulse duration could be widely tuned. The location of the soliton compression point in the fiber depends on the pump pulse parameters, and the FOCR wavelength depends on the position of said compression point due to the fiber taper. Given that the laser parameters themselves are intricately interrelated [25], it is essential to regard the entire laser-tapered fiber setup as a single strongly coupled nonlinear dynamical system. As will be shown below, our design allows generation of continuously tunable FOCR spanning the wavelength range 414–612 nm using a single nonlinear fiber and a single pump source with a fixed central wavelength. The principal idea behind our scheme is applicable to other wavelength ranges and waveguide types, and we believe the technique has considerable potential for improvement with optimized fiber and laser design. In particular, it may allow for very rapid wavelength tuning by purely electric control of the pump source, without any need for mechanical rearrangements.

Our scheme ultimately relies on the following facts. First, FOCR generation requires pump-to-FOCR phase matching, which dictates the resulting FOCR wavelength based on the pump pulse central wavelength and the fiber dispersion, as illustrated in Fig. 1(a). Second, the FOCR generation process is strongly power dependent, and is, hence, spatially localized around the point of maximum soliton compression of the pump pulse in the fiber, as seen from the numerical simulation in Fig. 1(b). In a tapered fiber, with the dispersion profile varying along the fiber length, the resulting FOCR wavelength will thus be determined by the local fiber dispersion properties at this maximum-compression point within the fiber. In its turn, the actual position of this point along the fiber length, and hence the resulting output wavelength of the Cherenkov laser, can be unambiguously and continuously determined simply by varying the duration and power of the input pump pulse, as illustrated in Fig. 1(c).

Figure 1(d) illustrates the parameter space for continuous ultra-wide tuning of the central wavelength of the fiber taper-based Cherenkov laser demonstrated in this work, which is defined by the energy and duration of the pump pulses derived form a mode-locked Yb-fiber laser. As the figure shows, for a given pulse duration there is a threshold energy for FOCR generation. Close to this threshold, low-noise spectrally isolated FOCR peaks appear, whereas a further increase of pump pulse energy leads to continuum formation and increased noise. Since our goal is to achieve low-noise FOCR peaked around a chosen central wavelength, it is clear from the figure that we need to control both pump pulse energy and duration. This is because one needs to achieve a pump pulse energy close to the FOCR generation threshold (which itself depends on the FOCR wavelength), while at the same time ensuring that the soliton compression happens at the right position within the taper. Further details on the calculation and the experiment are described below in the text.

While many variations on the above general principle can be envisioned, in the present paper we focus on the generation of femtosecond pulses continuously tunable over the visible spectrum in the 400–600 nm range. We chose this spectral range for its special importance for bio-photonics applications, which we foresee as one of the main beneficiaries of our new technology. There, such a wide tuning range will allow the user to easily match the central wavelength of the laser to both one- or two-photon absorption peaks of molecules of interest [26]. As a result, both single-photon [1,26,27] and multiphoton [26–32] microscopy can be conveniently performed with the same laser system and microscope without any setup readjustment.

Our experimental setup is illustrated in Fig. 2 (see Appendix A.3 for details). The pump laser is a standard-design mode-locked femtosecond Yb-fiber master oscillator power amplifier (MOPA) laser operating at 42 MHz repetition rate, with a central wavelength of 1035 nm, maximum pulse energies in excess of 10 nJ, and pulse durations tunable upwards from 90 fs [33]. The pump pulses are easily reshaped in terms of peak power, duration, and chirp by tuning the fiber amplifier and/or the compressor (shadowed box in Fig. 2). The structural profile of the PCF used in both the experiments and the simulations is shown in Appendix A.4.

Our numerical simulations are based on a generalized nonlinear Schrödinger equation adapted to tapered fibers [34], parameterized by plane-wave-based calculations of the PCF dispersion and effective area properties. In the simulations, we assume that the fiber structure is preserved through the taper, except for an overall scaling that follows the outer diameter of the fiber, which we can experimentally measure. Furthermore, we consider single-mode propagation of linearly polarized transform-limited Gaussian pulses, whose duration and power are varied. Birefringence may be included, but has been neglected in the presented results, because the birefringence of the PCF used in the experiments is unintentional and not well characterized. To obtain the desired spectrally smooth narrow-bandwidth FOCR pulses, the precise taper shape is found to play an important role. From theory, we expect the accelerated down-taper as shown in Fig. 2 to yield the cleanest FOCR pulse shapes, as explained in Appendix A.5, and such a taper was used in this work.

The upper panel of Fig. 3(a) shows the simulated FOCR spectra by pumping the designed down-tapered PCF with transform-limited Gaussian pulses at 1035 nm, and varying the duration and power of the pump pulses for FOCR tunability. The simulation results are also shown in Fig. 1(d), where the parameter space for the resulting laser output tunability—the 1035 nm pump pulse duration and energy—is presented. The experimentally obtained spectra between 414 and 612 nm are depicted in the lower panel of Fig. 3(a) and the corresponding experimental conditions (Appendix A.6, the power and duration of the input pump pulse) are shown in Fig. 1(d). As one can see, the broad laser tunability within ∼200nm spectral range is conveniently achieved by electrical control of the fiber amplifier power and the pulse compressor, with the experimental results closely matching the theoretical predictions.

In the above experiments, the laser output wavelength was tuned in a matter of seconds, by manually adjusting the amplifier gain and the compressor setting (see shadowed box in Fig. 2). Remarkably, even by adjusting the pump power alone, and keeping the compressor setting fixed, we could tune the laser wavelength over the 420–560 nm range, covering much of the visible spectrum. This constitutes a further simplification of the practical implementation of our technology, drastically speeding up the laser tuning process. Indeed, the electronic control of pump power allows its adjustment on ∼10μs timescale (Appendix A.7), and can, in principle, be scaled down even to nanoseconds with complementary modulation of the laser signal [35]. Such a capability to achieve fully electrical ultra-wideband tunability of a laser on a microsecond, eventually even sub-microsecond timescale, can enable a new class of demanding applications where high laser tuning rate is of essence.

Figure 3(b) shows the far-field mode profiles of the measured FOCR signals, which were observed to be stable, with no sign of higher-order mode admixture, although the PCF used was multimode at visible wavelengths. Figure 3(c), left panel, shows the experimental autocorrelations of the FOCR output, measured in the operational range of our autocorrelator, 500–600 nm. Just as expected from the simulations, we obtain smooth pulse spectral profiles with moderate variations in duration. In Fig. 3(c), right panel, the autocorrelation full width at half-maximum (FWHM) of Cherenkov pulses is shown as a function of their wavelength (blue dots), along with the corresponding values for the input pump pulses from a Yb-fiber laser at 1035 nm (red squares). For comparison, in the same figure the autocorrelation FWHM of the simulated FOCR pulses is shown (dashed blue line), being corrected for dispersive effects in the optical elements between the PCF and the autocorrelator in order to match the experimental conditions (Appendix A.8). We note that the simulated pulse durations at the fiber end facet were below 100 fs at all FOCR wavelengths, including the spectral range below 500 nm, for which the experimental data could not be obtained due to the limitations of our autocorrelator and related optics. These generated pulses are much shorter than what is typically produced by currently most-used spectrally sliced SC technology [32]. This means that higher pulse peak power can be achieved with comparable pulse energy, benefitting such applications of tunable ultrafast lasers as nonlinear spectroscopy and microscopy.

Our simulations quite accurately reproduce both the measured spectra of the Cherenkov output in the entire range of laser tunability, 414–612 nm [Figs. 1(d) and 3(a)], and the measured autocorrelations within the accessible experimental range above 500 nm, while predicting the output pulse duration with reasonable accuracy [Fig. 3(c), right panel]. This fact strongly supports the presented physical picture of widely tunable FOCR generation in fiber tapers. We note that our simulations are performed using an idealized Gaussian pump laser pulse shape, while in reality the pump pulses may have a more complicated time structure. Nevertheless, even using such a simplification in the modeling, a close agreement is achieved between the experimental data and the theoretical predictions.

We comment that the actual limits to wavelength tunability of the Cherenkov fiber laser are defined by the interplay between the pump wavelength and soliton peak power, as well as the fiber dispersion at the pump and target wavelengths [12], all of which can be engineered. To this end, the laser wavelength tunability exceeding 1 octave of frequencies using a single taper can be envisaged.

Figure 4(a) shows the generated FOCR output power, and the pump-to-FOCR power conversion efficiency of our laser system. The output power range 1–5.5 mW corresponds to pulse energies of ∼25–130pJ, easily satisfying the energy requirements for, e.g., nonlinear microscopy experiments [36]. The observed conversion efficiency of our widely tunable FOCR laser of a few percent is quite typical for this wavelength-conversion process [37,38].

The intensity noise of the light source is another key parameter for laser performance evaluation. Figure 4(b) shows the signal-to-noise ratio (SNR) of the output of our laser, which is 1–3 orders of magnitude better than the typical picosecond-pumped supercontinuum (ps-SC) source spectrally sliced to ∼10nm bandwidth [38]. We note that spectral slicing of our Cherenkov laser to the same ∼10nm bandwidth around its peak wavelength will reduce its SNR by only an additional factor of 2. Therefore, using the tunable Cherenkov laser, the spectroscopy or imaging data of the same quality can be obtained up to 2–4 orders of magnitude faster, as compared to the ps-SC source of the same ∼10nm bandwidth, clearly demonstrating a significant practical advantage of widely tunable Cherenkov laser technology. The details of laser noise characterization are presented in Appendix A.9. With regards to the spectral stability, we did not observe any noticeable spectral changes during the measurement periods typically lasting up to 10 min.

Generally, the FOCR noise is found to increase as the wavelength is shortened, which is theoretically expected because the short-wavelength generation requires higher pump soliton numbers, thus translating into higher noise [7]. By the same argument, for a given wavelength the SNR is found to decrease with increasing output FOCR power.

We have presented a novel technology for widely tunable and highly stable ultrafast fiber lasers, based on FOCR in fiber tapers. Adding only one passive new element, a fiber taper, to a standard pump pulsed laser allows one in a very simple manner to continuously and resonantly convert the fixed pump laser wavelength to any desired wavelength within an ultra-wide spectral range, in a single-mode output, with power conversion efficiency of a few percent, and with excellent noise characteristics as compared to existing approaches, such as spectrally sliced SC. Based on this idea, we demonstrated a femtosecond fiber laser continuously tunable over the 200 nm wide red–green–blue spectral range, emitting 100–200 fs pulses with pulse energies of ∼25–130pJ. Our measurements are in good agreement with parameter-free simulations.

Because of its modest requirements on pump pulse energy and duration, monolithic all-fiber integration of a widely tunable Cherenkov laser [22] is a straightforward technological perspective. The demonstrated basic principle of combining tailored PCF taper structures with agile femtosecond pump lasers, such as widely commercially available Yb-, Er-, or Tm-fiber lasers, could be implemented in many ways, to target the generation within different spectral and intensity ranges, as well as discrete wavelengths, multiple pulses, etc. For example, when pumped with a standard Er-fiber laser at 1550 nm, the Cherenkov femtosecond output with higher energy [39] as well as broader tunability could be generated. Our findings thus pave the way to practical applications of simple and inexpensive Cherenkov femtosecond fiber lasers with wide continuous tunability in industry, science, and medicine.

As one of the key applications for the demonstrated laser technology, we foresee bio-photonics, making use of one- and many-photon excitations, Raman processes, etc., in biological tissues as well as in specially added markers (see, e.g., Refs. [27,40]). Currently, substantial effort is being put into translating bio-spectroscopy techniques, demonstrated and tested in research laboratories, into clinical environments. Here, the widely tunable Cherenkov fiber lasers will satisfy most stringent requirements on enabling light sources, such as adjustment-free long lifetime operation, compactness and robustness, high operational stability, sufficiently fast wavelength tuning, and very low noise. This will drastically, by several orders of magnitude, minimize the acquisition time of high-quality imaging and spectroscopy data, as compared to existing laser technologies [14,24], thus enabling measurements that were unfeasible before. Potentially, a single widely tunable Cherenkov laser will be able to access the whole range of fluorophores (∼400–800nm) used both in confocal microscopy and superresolution microscopy, thereby providing a complete multimodality laser scanning solution in a translational environment.

Acknowledgment. The authors thank Ö. Akçaalan for taper cleaving, U. Møller, P. Elahi, and H. Kalaycıoğlu for providing equipment for the experiments, and I. Pavlov, M. Bonn, M. Grechko, and S. Parekh for valuable discussions.